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  1. Home
  2. Books
  3. Groups, Languages and Automata
  • Cited by 12
Publisher:
Cambridge University Press
Online publication date:
March 2017
Print publication year:
2017
Online ISBN:
9781316588246
DOI:
https://doi.org/10.1017/9781316588246
Subjects:
Mathematics (general), Mathematics, Algorithmics, Complexity, Computer Algebra, Computational Geometry, Computer Science, Algebra
Series:
London Mathematical Society Student Texts (88)
Information

Book description

Fascinating connections exist between group theory and automata theory, and a wide variety of them are discussed in this text. Automata can be used in group theory to encode complexity, to represent aspects of underlying geometry on a space on which a group acts, and to provide efficient algorithms for practical computation. There are also many applications in geometric group theory. The authors provide background material in each of these related areas, as well as exploring the connections along a number of strands that lead to the forefront of current research in geometric group theory. Examples studied in detail include hyperbolic groups, Euclidean groups, braid groups, Coxeter groups, Artin groups, and automata groups such as the Grigorchuk group. This book will be a convenient reference point for established mathematicians who need to understand background material for applications, and can serve as a textbook for research students in (geometric) group theory.

Reviews

'The authors study how automata can be used to determine whether a group has a solvable word problem or not. They give detailed explanations on how automata can be used in group theory to encode complexity, to represent certain aspects of the underlying geometry of a space on which a group acts, its relation to hyperbolic groups … it will convince the reader of the beauty and richness of Group Theory.'

Charles Traina Source: MAA Reviews

'There are copious references and separate indices for notation, subjects, and names of earlier researchers. In summary, this text (written by three experts on the subjects) is a mostly self-contained condensation of hundreds of individual articles. It will serve as a valuable one-stop resource for both researchers and students.'

Eric M. Freden Source: MathSciNet

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Contents

Contents
  • 1 - Group theory
    pp 3-35
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References
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